Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
The Topological Space $\calE^2_\rmT$.
Simple Closed Curves

Agata Darmochwal

Warsaw University, Bialystok

Yatsuka Nakamura

Shinshu University, Nagano
Summary.

Continuation of [7]. The fact that
the unit square is compact is shown in the beginning of the article. Next
the notion of simple closed curve is introduced. It is proved
that any simple closed curve can be divided into two independent parts
which are homeomorphic to unit interval ${\Bbb I}$.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[10]
[11]
[2]
[3]
[8]
[5]
[4]
[1]
[6]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Agata Darmochwal.
Compact spaces.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Agata Darmochwal.
The Euclidean space.
Journal of Formalized Mathematics,
3, 1991.
 [7]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs.
Journal of Formalized Mathematics,
3, 1991.
 [8]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received December 30, 1991
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